English

Effective normal basis theorem

Number Theory 2026-01-22 v1

Abstract

Let K be a finite Galois extension of Q. The normal basis theorem provides an element of K whose conjugates form a Q-basis of K. Here we obtain such an element with controlled size. This improves a recent result by Fukshansky and Jeong. By the way, we estimate Minkowski's minima of ideals of integers of number fields.

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Cite

@article{arxiv.2601.14856,
  title  = {Effective normal basis theorem},
  author = {Pascal Autissier},
  journal= {arXiv preprint arXiv:2601.14856},
  year   = {2026}
}

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